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22-Elec-A2 Systems and Control: May 2016

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Basic definitions and concepts of control (compulsory)
  2. Question 2 Marginal stability by root locus, Bode and Routh–Hurwitz (compulsory)
  3. Question 3 State space vs. transfer function; controllability, observability, steady-state error
  4. Question 4 Root-locus analysis, gain selection and dominant model
  5. Question 5 PID design by pole placement
  6. Question 6 Lead/Lag controller design by pole placement
  7. Question 7 Lead controller design in the frequency domain
  8. Question 8 Nyquist stability (Part A) and state-space response (Part B)

Start with Question 1 →

Paper format. National Exams, 07-Elec-A2 Systems & Control, May 2016, 3 hours, closed book (approved Casio/Sharp calculator plus one signed, double-sided 8.5 × 11" formula sheet; a Laplace-transform table and the standard ζ–overshoot and ζ–resonant-peak design plots are supplied). Questions 1 and 2 are compulsory; a complete paper is five questions, so candidates choose three of Q3–Q8. Each question is worth 20 marks. All eight are worked below so the set is a complete study resource.

Reference texts: N. S. Nise, Control Systems Engineering (7th ed., Wiley) — time response and second-order specs (Ch. 4), block reduction (Ch. 5), Routh–Hurwitz (Ch. 6), steady-state error and static error constants (Ch. 7), root locus (Ch. 8), PID and lead–lag design (Ch. 9–11), frequency response, Bode, Nyquist, gain/phase margins (Ch. 10–11), state space, controllability/observability (Ch. 3, 12); K. Ogata, Modern Control Engineering (5th ed., Prentice Hall) — dominant-poles modelling. All step responses, block diagrams, pole–zero maps, root loci, the Bode sketches and the Nyquist plot below are redrawn as inline figures.

Reading the supplied design charts. The percent overshoot chart uses $PO=100\,e^{-\zeta\pi/\sqrt{1-\zeta^2}}$ and the second-order model is $G_m(s)=K_{dc}\,\dfrac{\omega_n^2}{s^2+2\zeta\omega_n s+\omega_n^2}$; the figures on the exam paper (step responses, root loci, Bode plots) are read graphically, so the values below carry normal chart-reading tolerance.